details if you want them:
The laptop has a broken LCD, and only HDMI output. The laptop has been working, yet, enchanted a filesystem error and will no longer boot to Windows 10. It does display the circular-booting-animation on the HDMI, yet, never gets to Windows.

I tried a regular Windows 10 Recovery Boot USB drive, yet, it does not boot to HDMI.

I am hoping the ultimatebootcd will boot to HDMI, I have only used ultimatebootcd on VGA before.

Interesting question.
I would have to say the question is; will/can the PC (Towre or Laptop) output a HDMI signal using a bootable CD?

So, the question to you; if you connect a HDMI cable to a external monitor, can you see the BIOS/UEFI screen or anything durning the boot process? or is the only time you see video is while you are in the O/S (which I assume is Win 10)?